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Decimal to Binary

In this page we will learn about decimal to binary conversion.Binary number is number with base 2 and decimal number is a number with base 10.This conversion is very important because in computers the data is stored in binary format.and the user enters the number in decimal format so system will convert decimal to binary and store it.aLet us see what is a binary number and decimal number and conversion of decimal to binary.


Is this topic Binary Division  hard for you? Watch out for my coming posts. 


Binary numbers: 


Binaryrefers to characterized by or consisting of two parts or components.  The word binary denotes two (sections or subjects or values). The binary value in mathematics is having only two values 0s and 1s. The number which is expressed only in 0s and 1s are called binary numbers. The binary numbers are represented as that of decimal numbers. The numbers are placed left or right of the point. The numbers may be greater than one or less than one.


Decimal numbers:


Decimal number is a number which is formed with combination of two parts.one part is called integer part and other part is calledfractional part.part which exist left of decimal point is called integer part and part right of decimal point is called fractional part.for example.  5.36


here 5="integer" part

     36="fractional" part


How to convert decimal to binary:


step 1:Divide given number starting from 2 as suitable.

step 2:write remainder on the right side of quotient.

step 3:divide untill quotient will be 0.

step 4:now write binary number starting from lower end of that divison.

step 5:now write given number including quotient of lower end.that should be starting point.


Convert decimal to binary


Below are the problems based on how to convert decimal to binary -

Problem 1:

Convert 35 into binary number.

Solution:

 The binary number can be calculated by using L division method

                        2 | 35
                           -------
                        2 | 17  -- 1
                           -------
                        2 | 8    -- 1
                           -------
                        2 | 4     --0
                           -------
                        2 | 2   -- 0
                           --------
                             1   -- 0

The binary number of 35 is 1000112.

Problem 2:

Convert 65 into binary number.

Solution:

                       2 | 65
                           -------
                        2 | 32  -- 1
                           -------
                        2 |16   -- 0
                           -------
                        2 | 8    --0
                           -------
                        2 | 4   -- 0
                           --------
                         2 |   2   -- 0="1....0

So binary number of 65 is 1000001

Problem 3:

Convert 142 into decimal numbers.

Solution:

                        2 | 142
                           -------
                        2 | 71  -- 0
                           -------
                        2 | 35  -- 1
                           -------
                        2 | 17   -- 1
                           -------
                        2 | 8     -- 1
                           --------
                        2 | 4     -- 0
                           ---------
                       2 |  2    --  0
                          ----------
                             1    -- 0

Fromthe above conversion, we divide the given decimal number by the base (2) and get the remainder. Then the remainders all are considered from bottom to top to get the binary value of the decimal number.This way, wecan convert the decimal to binary.

The binary number of 142 is 100011102


I am planning to write more post on samacheer kalvi 10th maths book  and Convert a Decimal to a Fraction. Keep checking my blog. 


Practice problem


Problem 1:

 Convert the following decimal number into binary number: 56

Solution: 111000

Problem 2:

Convert the following decimal number into binary number: 32

Solution: 100000

Problem 3:

Convert the following decimal number into binary number: 78

Solution: 1001110

Problem 4:

Convert the following decimal number into binary number: 158  

Solution: 10011110